Volume 15, Number 1 (2016) | JIRSS 2016, 15(1): 59-70 | Back to browse issues page

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Khanjari Sadegh M. Distribution of Order Statistics for Exchangeable Random Variables. JIRSS. 2016; 15 (1) :59-70
URL: http://jirss.irstat.ir/article-1-365-en.html

Department of Statistics‎, ‎University of Birjand‎, ‎Birjand‎, ‎Iran
Abstract:   (1110 Views)

Let T1,...,Tn be exchangeable random variables and suppose that T{1:n} represents the ith order statistic among Ti's, i=1,...,n. ‎In this paper some expressions for the joint distribution ‎of (T{1:n},...,T{n:n}), ‎marginal distribution of T{1:n} and the joint distribution of (T{r:n},T{k:n}), 1≤ r ≤ k ≤n ‎in terms of the joint distribution (or joint reliability) function of Ti's are provided. ‎Using these and when {T1,...,Tn} is a sequence of‎ ‎lifetimes, some expressions for the mean residual life functions of a n-k+1-out-of-n system‎, Hnk(t)=E(T{k:n}-t|T{1:n}>t) and Mn{r,k}(t)=E(T{k:n}-t|T{r:n}>t), ‎1≤ r≤ k≤ n in terms of the joint survival function of Ti's are given‎. ‎Also, ‎some examples are provided‎. 

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Type of Study: Original Paper | Subject: 62Fxx: Parametric inference
Received: 2016/08/2 | Accepted: 2016/08/2 | Published: 2016/08/2

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